Finite Group Databasebeta

← #14764838

Subgroups — #14764838

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622742C211yesmaximal, characteristic, complemented
3#13071831C211yesmaximal, characteristic
4#13069412C212yesmaximal, complemented
5#13069230C212yesmaximal, complemented
6#13069227C212yesmaximal, complemented
7#13068911C212yesmaximal, complemented
8#13068799C211yesmaximal, characteristic, complemented
9#13068527C211yesmaximal, characteristic, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1870C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×C22⋊D11C2212yes—
16C22×#4318C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2212yes—
20#10622836C412yes—
21C4×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622742—24no—
25C2×(C2×D11)⋊C8C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66879C2212yes—
30C2×Dic11⋊C8C2212yes—
31#10622624—24no—
32#10622604C411yescharacteristic
33#10622592C411yescharacteristic
34#10622573C411yescharacteristic
35#10622572C412yes—
36#10622560C411yescharacteristic
37C4×(C2×D11)⋊C4C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40C11×#336C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43C22×D4×C11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11C2×C412yes—
47C22×C22⋊D11C2×C412yes—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—42no—
51C2×#4339—42no—
52C22×D44C2×C411yescharacteristic
53C22×C4×D11C2312yes—
54C22×Dic22C2×C411yescharacteristic
55C2×C11×M16—22no—
56C2×C11×M16—42no—
57C22×C8×C11C2312yes—
58C22×C8×C11C2312yes—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11C2×C412yes—
66C2×C22⋊Dic11C2×C412yes—
67C4×C22⋊D11—42no—
68C4×C22⋊D11—42no—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×C4×Dic11C2312yes—
74C2×#4318—22no—
75C2×#4318—42no—
76C22×C11⋊C8—42no—
77C22×C11⋊C8D414yescomplemented
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C11×C22⋊C8—22no—
83C11×C22⋊C8—42no—
84C11⋊#95C2×C412yes—
85C11⋊#95C2×C412yes—
86C11⋊#95C2×C411yescharacteristic
87C11⋊#95C2×C411yescharacteristic
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)—22no—
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—24no—
92(C2×D11)⋊C8—42no—
93(C2×D11)⋊C8—42no—
94#66879—42no—
95Dic11⋊C8—42no—
96C4⋊(C11⋊C8)—22no—
97#66867—22no—
98#22035—111nomaximal, Sylow
99C24×C11C22×C411yescharacteristic
100C24×C11C22×C411yescharacteristic
101C23×D11C22×C412yes—
102C2×D4×C11—22no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C2×C22⋊D11—42no—
123C2×C22⋊D11—42no—
124C22×Dic11C22×C412yes—
125C22×Dic11C22×C412yes—
126C22×Dic11C22×C412yes—
127#4339—44no—
128#4339—44no—
129#4339—48no—
130C2×D44—22no—
131C2×D44—42no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×Dic22—22no—
139C2×Dic22—42no—
140C11×M16—44no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C11×C4⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11—21no—
151C42×C11—21no—
152C22⋊Dic11—42no—
153C22⋊Dic11—42no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157Dic11⋊C4—42no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160#4318—44no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—44no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170C2×#435—111no—
171C2×#408—111no—
172#2388—111no—
173#1955—112no—
174#1924—112no—
175#1924—112no—
176#1870—112no—
177#1870D1111yescharacteristic, complemented
178#1851—111no—
179#1780—111no—
180#1752—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—22no—
187C23×C11—21no—
188C23×C11—22no—
189C23×C11—21no—
190C23×C11C4×D412yes—
191C23×C11C23×C411yescharacteristic
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199D4×C11—44no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11C4×D412yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C2×C4×C11H(5,𝔽2)12yes—
219C22⋊D11—48no—
220C22⋊D11—48no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230D44—44no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C4×D11—42no—
235Dic22—44no—
236C8×C11—42no—
237C8×C11—42no—
238C11⋊C8—22no—
239C11⋊C8—22no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C22×#41—111no—
243C22×M16—111no—
244C22×M16C2×D1111yescharacteristic
245C23×C8—111no—
246C2×C4×D4—112no—
247C2×C4×D4C2×D1111yescharacteristic
248#435—224no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8—112no—
251#408—224no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8—111no—
254C2×C22⋊C8—112no—
255C2×C22⋊C8—112no—
256C2×C22⋊C8—112no—
257C2×C22⋊C8—112no—
258C2×C22⋊C8C2×D1111yescharacteristic
259C2×C22⋊C8C2×D1112yes—
260C2×#97—111no—
261C2×#97—112no—
262#395—111no—
263#394—111no—
264#394—112no—
265#393—111no—
266#392—112no—
267#392—111no—
268C4×C22⋊C4—111no—
269C4×C22⋊C4—112no—
270#336—112no—
271#336—112no—
272#336C2×D1112yes—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11C2×C4×D411yescharacteristic
284C22×C11#51812yes—
285C22×C11#56811yescharacteristic
286C22×C11#56811yescharacteristic
287C22×C11#56812yes—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C4×C11—22no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11#53411yescharacteristic
300C4×C11#53511yescharacteristic
301C4×C11#53812yes—
302Dic11—42no—
303Dic11—42no—
304Dic11—42no—
305C2×#41—222no—
306C2×#41—222no—
307C2×#41—442no—
308C2×#41—442no—
309C22×Q8—111no—
310C22×D4—112no—
311C22×D4—112no—
312C22×D4—111no—
313C22×D4C4×D1111yescharacteristic
314C23×C4—112no—
315C23×C4C22×D1111yescharacteristic
316C23×C4C22×D1111yescharacteristic
317C2×M16—22no—
318C2×M16—42no—
319C2×M16—222no—
320C2×M16—442no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—114no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—442no—
327C22×C8C22×D1112yes—
328C22×C8C22×D1112yes—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—442no—
332C4×D4—442no—
333C2×C4⋊C4—112no—
334C2×C4⋊C4C4×D1111yescharacteristic
335C2×C22⋊C4—112no—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—112no—
339C2×C22⋊C4—112no—
340C2×C22⋊C4C4×D1111yescharacteristic
341C2×C22⋊C4C4×D1111yescharacteristic
342C2×C42—112no—
343C2×C42C22×D1111yescharacteristic
344C4⋊C8—222no—
345C4⋊C8—442no—
346C22⋊C8—22no—
347C22⋊C8—42no—
348C22⋊C8—224no—
349C22⋊C8—224no—
350C22⋊C8—222no—
351C22⋊C8—222no—
352C22⋊C8—442no—
353C22⋊C8—442no—
354#97—222no—
355#97—442no—
356#95—111no—
357#95—112no—
358#95—111no—
359#95—112no—
360C2×C11—42no—
361C2×C11—81no—
362C2×C11#232111yescharacteristic
363C2×C11#293011yescharacteristic
364C2×C11#293211yescharacteristic
365C2×C11#297812yes—
366C2×C11#298012yes—
367D11—82no—
368C24—112no—
369C24C2×C4×D1111yescharacteristic
370C24C2×C4×D1111yescharacteristic
371#41—444no—
372#41—448no—
373#41—444no—
374C2×Q8—222no—
375C2×Q8—442no—
376C2×D4—22no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—224no—
380C2×D4—222no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4C2×C4×D1111yescharacteristic
403C22×C4C2×C4×D1111yescharacteristic
404C22×C4C2×C4×D1111yescharacteristic
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4D4×D1112yes—
407C22×C4#434112yes—
408C22×C4C23×D1111yescharacteristic
409M16—44no—
410M16—444no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—112no—
418C2×C8—112no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—221no—
422C2×C8—221no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—444no—
426C4⋊C4—22no—
427C4⋊C4—442no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—442no—
431C22⋊C4—442no—
432C22⋊C4—442no—
433C22⋊C4—442no—
434C22⋊C4—442no—
435C42—21no—
436C42—21no—
437C42—222no—
438C42—222no—
439C11#2203511yescharacteristic, complemented, Sylow
440C23—21no—
441C23—21no—
442C23—22no—
443C23—22no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—22no—
448C23—22no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—222no—
453C23—222no—
454C23—222no—
455C23—222no—
456C23(C22⋊D11)⋊C412yes—
457C23C22×C4×D1111yescharacteristic
458Q8—444no—
459D4—44no—
460D4—444no—
461D4—448no—
462D4—448no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4(C22⋊D11)⋊C412yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×#434111yescharacteristic
493C2×C4#6703712yes—
494C2×C4#6704212yes—
495C8—42no—
496C8—42no—
497C8—222no—
498C8—222no—
499C8—441no—
500C8—441no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—41no—
510C22—42no—
511C22—442no—
512C22—442no—
513C22—442no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—442no—
518C22C2×(C22⋊D11)⋊C411yescharacteristic
519C22#1062307612yes—
520C22#1062327611yescharacteristic
521C22#1062327611yescharacteristic
522C22#1062328112yes—
523C4—22no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—442no—
528C4—442no—
529C4—442no—
530C4#1062312311yescharacteristic
531C4#1062314812yes—
532C4#1062318411yescharacteristic
533C2—42no—
534C2—81no—
535C2—882no—
536C2#1307127911yescharacteristic
537C2#1307731511yescharacteristic
538C2#1307733111yescharacteristic
539C2#1307767312yes—
540C2#1307768412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radical#13071831C2
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22035
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622742C2semidirect
4. #13069412C2semidirect
5. #13069230C2semidirect
6. #13069227C2semidirect
7. #13068911C2semidirect
8. #13068799C2semidirect
9. #13068527C2semidirect
10. #13068395C2semidirect
11. C11×#1870C2semidirect
77. C22×C11⋊C8D4semidirect
177. #1870D11semidirect
439. C11#22035semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226242
C2×#106227422
#130718312
#130694122
#130692302
#130692272
#130689112
#130687992
#130685272
#130683952
C11×#18702
#2203511